The integral formula for secant is often introduced in a very artificial way. In this post, I look at the history of this integral and give several derivations.
For many calculus students, Riemann sums are those annoying things that show up in the derivation of the arc length formula.
In truth, these handy sums have done so much more. In this post, I’ll give some examples of Riemann sums dating from before the birth of calculus and some applications of Riemann sums that are still used today.
Our modern calendar, the Gregorian calendar, introduced several changes to the Julian calendar, including the introduction of a three-step algorithm for determining leap years.
But just how accurate is the Gregorian model? Can centuries of mathematics and astronomy lead us to a more accurate calendar?